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Topics from the 8th Annual UNCG Regional Mathematics and Statistics Conference pp 147–154Cite as

A Spatially Organized Population Model to Study the Evolution of Cooperation in Species with Discrete Life-History Stages

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 64))

Abstract

The evolution of cooperation and altruism has been addressed by numerous empirical and theoretical studies. Highlighting the associated theoretical problems and solutions, the simple Prisoner’s Dilemma has developed into the central research paradigm. Numerous variations have been developed to better reflect biological reality, including spatial and temporal aspects. Here, we develop a spatially structured population model to evaluate the impact of life history on the evolution of cooperation under a Prisoner’s Dilemma premise. Individuals occupy nodes of a square lattice and repeatedly interact with neighboring individuals according to fixed cooperation or defection rules. Individuals age and transition through different life history stage until death. Competitive, asexual reproduction occurs according to benefits gained during the Prisoner’s Dilemma interactions. Offspring inherit its parent’s behavioral strategy and the number of cooperators and defectors can be followed over time. Here, we report on the first set of experimental outcomes of this model, reconfirming the benefit of spatial structure for the evolution of cooperation. Secondly, we report that the model’s results present the combined outcome of the intrinsic, relative cost of cooperation and the system’s stochasticity because incipient groups of cooperators may be eliminated from the population by chance even though they enjoy a higher fitness than the predominant defector genotype. This is particularly clear when comparing simulations with neighborhoods of four and eight, which yield different results despite identical fitness payoff matrices and life history structure. In sum, this model presents a realistic tool to systematically evaluate the importance of life history on the evolution of cooperation, which has not been evaluated, but seems important because social species are often longer-lived than asocial species and some even exhibit a post-reproductive lifespan.

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Acknowledgments

The research was supported by an NSF grants DMS 0850465 and DBI 0926288. The authors wish to thank Kayla Jackson for her initial input in the development of the early stages of the model.

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Authors and Affiliations

  1. Department of Computer Sciences, The University of North Carolina at Greensboro, Greensboro, NC, 27402, USA

    Caitlin Ross

  2. Department of Biology, The University of North Carolina at Greensboro, Greensboro, NC, 27402, USA

    Olav Rueppell

  3. Department of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC, 27402, USA

    Jan Rychtář

Authors
  1. Caitlin Ross
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  2. Olav Rueppell
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  3. Jan Rychtář
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Corresponding author

Correspondence to Olav Rueppell .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics & Statistics, University of North Carolina at Greensboro, Greensboro, North Carolina, USA

    Jan Rychtář

  2. Dept. of Mathematics & Statistics, University of North Carolina at Greensboro, Greensboro, North Carolina, USA

    Sat Gupta

  3. Dept. of Mathematics & Statistics, University of North Carolina at Greensboro, Greensboro, North Carolina, USA

    Ratnasingham Shivaji

  4. Dept. of Mathematics & Statistics, University of North Carolina at Greensboro, Greensboro, North Carolina, USA

    Maya Chhetri

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Ross, C., Rueppell, O., Rychtář, J. (2013). A Spatially Organized Population Model to Study the Evolution of Cooperation in Species with Discrete Life-History Stages. In: Rychtář, J., Gupta, S., Shivaji, R., Chhetri, M. (eds) Topics from the 8th Annual UNCG Regional Mathematics and Statistics Conference. Springer Proceedings in Mathematics & Statistics, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9332-7_15

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